Aaron Brown

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The English word is taken from the German statistik, which was invented by Gottfried Aschenwall and used in his 1748 work Vorbereitung zur Staatswissenschaft. Aschenwall’s sta-

tistiks had nothing to do with either numbers or probability. They referred to qualitative reports compiled by agents of a monarch to describe the resources available to him. German political scientists were hostile to numerical data for this purpose because they could not capture essential detail. Adding up total population, for example, lumped together men, women, and children with different skills and social positions, possi-bly speaking different languages, and following different religions. Without a large bureaucracy to cross-tabulate and analyze data, the prince and his few advisors needed focused qualitative reports more than lists of numbers.

The word worked its way over to France as statistiques. In addition to three extra letters for the same sound, the word acquired a different

connotation. After the Revolution, France was interested in rationalizing itself, which required measuring everything according to common standards. Part of this effort involved sending questionnaires to the préfets of each département. These mixed quantitative and qualitative infor-mation, but even the qualitative information was categorized. That is, the préfets were given

StatistiksWhy do we use the same word, statistics, for numbers put out by the government and the science of applied probability? This question turns out to have a very interesting answer, one that sheds light on attitudes toward quants

systematic questionnaires with boxes in which either numbers or words could be written. The idea was to uncover the ideal of Frenchness, for which the average was usually the best statistic. Individual observations were regarded as error, noise around mean.

This difference came down to a different con-ception of the State. In pre-Bismarck Germany,

Great advances made in statistical accuracy

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the State had no real legitimacy. There was a prince, and there was some territory he control-led. The prince wanted information about the territory to use for his own benefit. France, on the other hand, was a State of unquestioned legitima-cy. Everyone knew there was a France. They might not agree on who ran the place, or even whether the government was a monarchy, republic, or empire, but they didn’t dispute that there was a distinct group of people who shared a language and a culture and lived in a patch of Europe with vague borders. The French State wanted informa-tion about itself.

England was somewhere in between. For one thing, it was a united (in theory anyway) kingdom of peoples with different languages, religions, and cultures. For another, it lacked the absolutist tradition of France. Britain was an overlapping set of institutions rather than an integrated totality that defined all its subjects. The government lost interest in compiling demo-graphic information after the Domesday Book in 1085 (ordered by a French Norman). Therefore it fell to private amateurs to develop political arith-metic. This involved both the compilation and analysis of data. Moreover, in England the entire distribution was studied, not just the mean.

The United States developed in a fourth way. Article 1, Section 2 of the Constitution set the tone by ordering a decennial census used to determine tax assessments and political rep-resentation. The two were linked explicitly to give States competing incentives for overcount or undercount. This is the section with the infa-mous provision to count slaves as three-fifths of a free person (less well known, Native Americans were counted as zero). This was not an evaluation of the human worth of slaves, it was a political compromise between free and slave states to apportion taxes and votes. Government num-bers were computed in rigid ways to mediate among differing interest groups. To this day, the census must be an enumeration of individuals. Sampling methods would be far cheaper and pos-sibly more accurate (certainly insisting on enu-meration results in some systematic biases) but would open the process up to subjectivity.

Whenever the American Congress has found itself overwhelmed by narrow political interests

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and unable to make rational national decisions, it creates an elite group of objective experts to analyze data. Prominent examples are the Army Corps of Engineers that has to pass on all nation-al water projects, and the Congressional Budget Office to provide one set of numbers for fiscal decisions. These groups are never given power, they are only supposed to provide objective analy-sis according to politicized rules laid down at the beginning. But because they are not political, or more accurately because they have been pre-balanced for political neutrality, their findings carry tremendous weight as natural points of compromise.

An ironic example of the American obses-sion for objectivity over truth began in 1933 when the newly created Securities and

Exchange Commission ordered all public companies to prepare financial statements according to strict rules, and hire independent auditors to certify that the rules were followed. A notorious example of the rules was that all assets were to be valued at historical cost minus pro forma depreciation rather than current value, which had been the usual practice. The SEC wanted objective numbers, not accurate ones. Companies protested that forcing all enterprises into a single format would lead to distortion, but they were overruled. Seventy years later the SEC, and most of the world, decided that public corporations had defrauded the public by issuing misleading ‘rules-based’ financial statements when every honest person knew that ‘principles-based’ statements were required; and that it was meaningless to have an independent auditor sign off that the rules were

followed, the CEO and CFO would be required to sign off that statements were accurate. In a dou-bly ironic move, the government decided to cre-ate principles-based accounting with a gigantic new set of rigid rules.

These four national streams fused to create modern statistics in both senses. I organize it by national tradition for ease of exposition. Of course there were contributions from other nations, and citizens of all four nations named contributed to all four traditions. Nevertheless, it is possible to see the differences in national atti-tudes toward numbers to this day.

The German and French traditions require data collected by someone loyal, to the prince or France respectively, and the results are confiden-tial, to the prince or the bureaucracy respectively.

In both cases the goal is to improve management of the State, for the benefit of the prince or the State respectively. The British and American traditions require the opposite. Statistics must be gathered by disinterested people and are pub-lished openly. The British goal is scientific inves-tigation to get at the truth. The American goal is to settle disputes.

The German and British traditions rely on investigators who are not employed by the gov-ernment. These people need some expertise in their area of investigation, but not rigorous spe-cialized training. The French and American tradi-tions instead use government-employed experts, generally selected by competitive examination from designated educational institutions.

To highlight the differences, consider statis-tics on unemployment. At any point in time there are people with full-time jobs, people with part-

These four national streams fused to create modern statistics in both senses... Nevertheless, it is possible to see the differences in national attitudes toward numbers to this day

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time jobs, people without jobs who don’t want them, people without jobs who do want them, people who are unemployable at any wage they would accept, seasonal workers, people with jobs who expect to lose them soon, people with jobs they hate or that do not provide a decent income, people who have off-the-books jobs, people who derive income from past work (like an author earning royalties) but who are not currently cre-ating new income, people working on projects that do not provide current income (like an as-yet-unpublished author), and many other situa-tions or permutations.

In the American tradition, this led to strong political resistance against computing an unem-ployment number in the first place. Doing so

would necessarily aggregate people in very differ-ent circumstances and require discretion on the part of compilers – discretion that could be used to someone’s political advantage. When that resistance was overcome during the Depression, rigid definitions were chosen. The point wasn’t to get at the true nature of unemployment, but to produce an objective number that could serve as the basis of political bargains. To this day, the United States does not count people who are unemployed but have given up looking for a job, and relies on new claims for unemploy-ment insurance, which can be measured easily but has a complex relation to unemployment. The unemployment rate figures into the Federal Reserve’s mandate and there are unwritten politi-cal rules for policies that are required at times of high measured unemployment. For example, when unemployment rises above six percent, it is assumed that many of the unemployed can-not find work, so unemployment compensation times are extended.

44 Wilmott magazine

The German tradition does not require aggre-gation. Unemployment would be studied by sending investigators to observe all aspects of the problem. Different people would be unemployed for different reasons, and suffering to varying degrees (some not at all). In this worldview, there is no such thing as unemployment, just people without jobs. Since there is never a short-age of things to do – either for the prince or, in modern times, for the State – unemployment can be cured easily. The jobless can be drafted, or ordered to work on projects, or otherwise employed.

In the English tradition, unemployment can be studied through many statistics to get at its multiple aspects. But there is a strict separa-

tion between observation and theory. Everyone should agree on the data, it should be able to be replicated. Two investigators collecting data should get the same result, even if the result has different interpretations in their respective theo-ries. Alone among the four traditions, the work need not lead to policy prescriptions. The goal is to publish the truth, someone else can worry about what to do in response.

In the French tradition, there is a social fact of an unemployment rate. That rate will affect different people differently. If the rate is high, A might lose his job, B might decide to stay in a safe government job rather than trying to start a busi-ness, C might stay in school to collect another degree rather than go on the job market, and D’s temp services business may thrive. A, B, C, and D are all noisy observations of a social reality. Statistics should collect and refine the data to alert all bureaucrats to the social fact. Then indi-vidual bureaucrats can make specific decisions appropriate to the situation.

All four traditions are alive and well in finance. The modern version of the German atti-tude is no longer hostile to numbers. Computers and armies of bureaucrats make numbers poten-tially useful. But numbers are descriptive and illustrative, they are not the reality. A useful report can have charts and figures, but the quant who buries herself in only the charts and figures is blind and dangerous. This is what many people have in mind when they say that quants destroyed the financial system.

The French tradition lives on in central banks and financial regulators. They collect huge vol-umes of mostly quantitative data, and hire highly-trained experts to interpret them. Most of this is secret, although they do deign to publish some summary values. The experts are universalist, like the metric system. The economic statistics are meaningful in themselves: there are true unem-ployment rates, inflation rates, and interest rates; these are social facts that affect everyone.

Since both these traditions assume analysts with points of view and are secretive, they tend to invite general distrust. Someone whose argument weaves a lot of special-purpose statistics that can-not be validated independently is not believed. “All figures don’t lie, but all liars figure”, as the saying goes. A secretive group of mandarins mak-ing decisions for everyone’s best interest is perfect fodder for conspiracy theories. Therefore, these types of quants need strong prestige to succeed.

The British and American traditions substi-tute a claim to objectivity for a claim of expertise. You don’t need to trust them because they are open about their data and methodology. You can replicate their results yourself. The British tradition is the scientific quant, the American tradition is the quant arbitrator. If you take the British approach, you lack power. All you can do is publish results and hope people are convinced by them. The American quant has power to make decisions, but those decisions are strongly con-strained by the need to be transparent and disinterested.

When people say ‘statistics’ today, they may mean any of the four traditions, or some amalgam of them. Statistics carries a lot of historical bag-gage, from the nature of reality to the power of the State to the definition of fairness and truth.

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Statistics carries a lot of historical baggage, from the nature of reality to the power of the State to the definition of fairness and truth

Models. Behaving. Badly.Why Confusing Illusion with Reality Can Lead to Disaster, on Wall Street and in LifeEmanuel Derman“Emanuel Derman has written my kind of book, an elegant combination of memoir, confession, essay on ethics, philosophy of science, and professional practice. He convincingly establishes the difference between model and theory and shows why attempts to model financial markets can never be genuinely scientific. It vindicates those of us who hold that financial modeling is neither practical nor scientific. Exceedingly readable.”—Nassim N. Taleb, author of The Black Swan

In this penetrating, insider’s look at the recent economic collapse, Emanuel Derman--former head quant at Goldman Sachs and a former physicist--explains the collision between mathematical modeling and economics that has touched every one of us. Though financial models imitate the style of physics and employ the language of mathematics, there is a fundamental difference between the aims and potential achievements of physics and those of finance. In physics, theories aim for a description of reality; in finance, at best, models can shoot only for a simplistic and very limited approximation of reality.

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In The Number That Killed Us, risk management and derivatives guru Pablo Triana presents a shocking look at Value at Risk (VaR), the mathematical model that encouraged banks to take on toxic assets they should never have touched and that ultimately brought the international financial system to its knees.

Essential reading for individual and professional investors, market professionals, regulators, policymakers, and anyone who wants to really understand where all the money went, The Number That Killed Us drags the risk measurement tool that has repeatedly and severely hurt the financial world into the spotlight.

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Frequently Asked Questions in Quantitative Finance2nd EditionPaul Wilmott “Getting agreement between finance theory and finance practice is important like never before. In the last decade the derivatives business has grown to a staggering size, such that the outstanding notional of all contracts is now many multiples of the underlying world economy. No longer are derivatives for helping people control and manage their financial risks from other business and industries, no, it seems that the people are toiling away in the fields to keep the derivatives market afloat! (Apologies for the mixed metaphor!) If you work in derivatives, risk, development, trading, etc. you’d better know what you are doing, there’s now a big responsibility on your shoulders.

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…And that’s what this book is about.”

978-0-470-74875-6 • Paperback • 624 pages September 2009 • £29.99 / €36.00 £17.99 / €21.60

Red-Blooded RiskThe Secret History of Wall StreetAaron BrownEveryone talks about risk, but few people give serious thought to what risk is. It’s hard to describe it without expressing an opinion—we like things that are innovative, daring, creative, and bold; but those are exactly the same things that are reckless, speculative, risky, and irresponsible.

This book will change the way you think about everything from history, risk, and money to vampires, zombies, and tulips. It offers a fascinating and thrilling account of great events that have never before been described in an easily accessible form. There are bold ideas, colorful characters, and, most important, the keys to understanding the modern financial world and how its inner workings affect our daily lives.

978-1-1180-4386-8 • Hardback • 432 pages • November 2011 • £23.99 / €28.00 £14.39 / €16.80